23,373 research outputs found
Locally Encodable and Decodable Codes for Distributed Storage Systems
We consider the locality of encoding and decoding operations in distributed
storage systems (DSS), and propose a new class of codes, called locally
encodable and decodable codes (LEDC), that provides a higher degree of
operational locality compared to currently known codes. For a given locality
structure, we derive an upper bound on the global distance and demonstrate the
existence of an optimal LEDC for sufficiently large field size. In addition, we
also construct two families of optimal LEDC for fields with size linear in code
length.Comment: 7 page
Optimal Locally Repairable Codes and Connections to Matroid Theory
Petabyte-scale distributed storage systems are currently transitioning to
erasure codes to achieve higher storage efficiency. Classical codes like
Reed-Solomon are highly sub-optimal for distributed environments due to their
high overhead in single-failure events. Locally Repairable Codes (LRCs) form a
new family of codes that are repair efficient. In particular, LRCs minimize the
number of nodes participating in single node repairs during which they generate
small network traffic. Two large-scale distributed storage systems have already
implemented different types of LRCs: Windows Azure Storage and the Hadoop
Distributed File System RAID used by Facebook. The fundamental bounds for LRCs,
namely the best possible distance for a given code locality, were recently
discovered, but few explicit constructions exist. In this work, we present an
explicit and optimal LRCs that are simple to construct. Our construction is
based on grouping Reed-Solomon (RS) coded symbols to obtain RS coded symbols
over a larger finite field. We then partition these RS symbols in small groups,
and re-encode them using a simple local code that offers low repair locality.
For the analysis of the optimality of the code, we derive a new result on the
matroid represented by the code generator matrix.Comment: Submitted for publication, a shorter version was presented at ISIT
201
Codes With Hierarchical Locality
In this paper, we study the notion of {\em codes with hierarchical locality}
that is identified as another approach to local recovery from multiple
erasures. The well-known class of {\em codes with locality} is said to possess
hierarchical locality with a single level. In a {\em code with two-level
hierarchical locality}, every symbol is protected by an inner-most local code,
and another middle-level code of larger dimension containing the local code. We
first consider codes with two levels of hierarchical locality, derive an upper
bound on the minimum distance, and provide optimal code constructions of low
field-size under certain parameter sets. Subsequently, we generalize both the
bound and the constructions to hierarchical locality of arbitrary levels.Comment: 12 pages, submitted to ISIT 201
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